Merging multiple OBJ files into one file with shape keys
You can use this script to accomplish an obj sequence import to shapekeys.
Paste the script into the text editor in blender, and click the Run Script button. 

This will add a new command in the file menu called File>Import>OBJ as Shapekey. Select your target object, and then run the new command.



bl_info = {
    'name': 'Load Obj Sequence as Shape Keys',
    'author': 'cmomoney',
    'version': (0, 2),
    'blender': (2, 6, 7),
    'category': 'Import-Export',
    'location': 'File &gt; Import/Export',
    'wiki_url': ''}

# ##### BEGIN GPL LICENSE BLOCK #####
#
#  This program is free software; you can redistribute it and/or
#  modify it under the terms of the GNU General Public License
#  as published by the Free Software Foundation; either version 2
#  of the License, or (at your option) any later version.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#
#  You should have received a copy of the GNU General Public License
#  along with this program; if not, write to the Free Software Foundation,
#  Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# ##### END GPL LICENSE BLOCK #####

import bpy, os
from bpy.props import *

class LoadObjAsShapekey(bpy.types.Operator):
    bl_idname = 'load.obj_as_shapekey'
    bl_label = 'Import OBJ as Shape Keys'
    bl_options = {'REGISTER', 'UNDO'}
    bl_description = "Import Obj sequence as shape key(s)"

    filepath = StringProperty(name="File path", description="File filepath of Obj", maxlen=4096, default="")
    filter_folder = BoolProperty(name="Filter folders", description="", default=True, options={'HIDDEN'})
    filter_glob = StringProperty(default="*.obj", options={'HIDDEN'})
    files = CollectionProperty(name='File path', type=bpy.types.OperatorFileListElement)
    filename_ext = '.obj'

    @classmethod
    def poll(cls, context):
        return context.active_object is not None and context.active_object.type == 'MESH'

    def execute(self, context):
        #get file names, sort, and set target mesh
        spath = os.path.split(self.filepath)
        files = [file.name for file in self.files]
        files.sort()
        target = bpy.context.scene.objects.active
        #add all ojs in sequence as shape  keys
        for f in files:
            fp = os.path.join(spath[0], f)
            self.load_obj(fp)
        #now delete objs
        sknames = [sk.name for sk in target.data.shape_keys.key_blocks]
        bpy.ops.object.select_all(action='DESELECT')
        for obj in sknames:
            if obj != 'Basis':
                target.data.shape_keys.key_blocks[obj].interpolation = 'KEY_LINEAR'
                bpy.context.scene.objects.active = bpy.data.objects[obj]
                bpy.data.objects[obj].select = True
                bpy.ops.object.delete()
            bpy.ops.object.select_all(action='DESELECT')
        #reselect target mesh and make active
        bpy.context.scene.objects.active = target
        target.select = True
        return{'FINISHED'}

    def invoke(self, context, event):
        wm = context.window_manager.fileselect_add(self)
        return {'RUNNING_MODAL'}

    def load_obj(self, fp):
        bpy.ops.import_scene.obj(filepath=fp,split_mode='OFF')
        bpy.ops.object.join_shapes()
        return

def menu_func_import(self, context):
    self.layout.operator(LoadObjAsShapekey.bl_idname, text="Obj As Shapekey(.obj)")

def register():
    bpy.utils.register_class(LoadObjAsShapekey)
    bpy.types.INFO_MT_file_import.append(menu_func_import)

def unregister():
    bpy.utils.unregister_class(LoadObjAsShapekey)
    bpy.types.INFO_MT_file_import.remove(menu_func_import)

if __name__ == "__main__":
    register()


Please note this is not my script, I'm just posting it here for convenience.